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 A299534 Solution b( ) of the complementary equation a(n) = b(n-1) + 2*b(n-2), where a(0) = 1, a(1) = 2; see Comments. 2
 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 87, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From the Bode-Harborth-Kimberling link: a(n) = b(n-1) + 2*b(n-2) for n > 2; b(0) = least positive integer not in {a(0),a(1)}; b(n) = least positive integer not in {a(0),...,a(n),b(0),...,b(n-1)} for n > 0. Note that (b(n)) is strictly increasing and is the complement of (a(n)). See A022424 for a guide to related sequences. LINKS J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264. MATHEMATICA mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; a[n_] := a[n] = b[n - 1] + 2*b[n - 2]; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 100}]    (* A296220 *) Table[b[n], {n, 0, 100}]    (* A299534 *) CROSSREFS Cf. A022424, A296220. Sequence in context: A039237 A039181 A298111 * A026454 A026458 A059109 Adjacent sequences:  A299531 A299532 A299533 * A299535 A299536 A299537 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 21 2018 STATUS approved

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Last modified September 20 11:01 EDT 2020. Contains 337264 sequences. (Running on oeis4.)